{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T18:16:10Z","timestamp":1769710570065,"version":"3.49.0"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>Permutation arrays under the Kendall-[Formula: see text] metric have been considered for error-correcting codes. Given [Formula: see text] and [Formula: see text], the task is to find a large permutation array of permutations on [Formula: see text] symbols with pairwise Kendall-[Formula: see text] distance at least [Formula: see text]. Let [Formula: see text] denote the maximum size of any permutation array of permutations on [Formula: see text] symbols with pairwise Kendall-[Formula: see text] distance [Formula: see text]. New algorithms and several theorems are presented, giving improved lower bounds for [Formula: see text]. Also, [Formula: see text]-arrays are defined, which are permutation arrays on [Formula: see text] symbols with Kendall-[Formula: see text] distance [Formula: see text], with the restriction that symbols [Formula: see text] appear in increasing order. Let [Formula: see text] denote the maximum size of any [Formula: see text]-array. For example, [Formula: see text]-arrays are useful for recursively computing lower bounds for [Formula: see text]. Lower and upper bounds are given for [Formula: see text].<\/jats:p>","DOI":"10.1142\/s179383092550020x","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:24:11Z","timestamp":1735604651000},"source":"Crossref","is-referenced-by-count":1,"title":["Bounds for permutation arrays under Kendall Tau metric"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2866-6766","authenticated-orcid":false,"given":"Sergey","family":"Bereg","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"Bumpass","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1219-5170","authenticated-orcid":false,"given":"Mohammadreza","family":"Haghpanah","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2795-9265","authenticated-orcid":false,"given":"Brian","family":"Malouf","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7192-9891","authenticated-orcid":false,"given":"I. Hal","family":"Sudborough","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"S179383092550020XBIB001","doi-asserted-by":"crossref","unstructured":"A. Abdollahi, J. Bagherian, F. Jafari, M. Khatami, F. Parvaresh and R. 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